On the Definition of Intuitionistic Fuzzy h-ideals of HemiringsRahman, Saifur; Saikia, Helen Kumari;

Abstract

Using the Lukasiewicz 3-valued implication operator, the notion of an ()-intuitionistic fuzzy left (right) -ideal of a hemiring is introduced, where . We define intuitionistic fuzzy left (right) -ideal with thresholds () of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right) -ideal with thresholds () and ()-intuitionistic fuzzy left (right) -ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a () (or () or ()-intuitionistic fuzzy left (right) -ideal of R if and only if A is an intuitionistic fuzzy left (right) -ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a () (or () or ())-intuitionistic fuzzy left (right) -ideal if and only if for any (0, 1] (or (0, 0.5] or (0.5, 1] ), is a fuzzy left (right) -ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right) -ideal with thresholds () of R if and only if for any , the cut set is a fuzzy left (right) -ideal of R.